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FULLY MODIFIED ESTIMATION OF SEASONALLY COINTEGRATED PROCESSES

Published online by Cambridge University Press:  05 March 2010

Stéphane Gregoir
Stéphane Gregoir*
Affiliation:
EDHEC Business School
*
*Address correspondence to Stéphane Gregoir, EDHEC Business School 12 bis rue de la victoire 75009 Paris, France; e-mail: [email protected].
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Abstract

We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as illustrated in Gregoir (1999a) and derive estimates of the cointegration vectors that allow for asymptotic normal inference. This allows us to propose a test whose null hypothesis is the existence of seasonal cointegration. A Monte Carlo exercise investigates the finite sample properties of this test procedure. The paper closes with the analysis of situations in which there exist more than one frequency at which seasonal cointegration can be observed.

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 5 , October 2010 , pp. 1491 - 1528
Copyright
Copyright © Cambridge University Press 2010

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